[math]\frac{dy}{dx}=\cos(y+f(x))[/math]

 

here y and f are functions of x .

 

highly non linear. tried maple. didnt give jack

[math]\frac{dy}{dx}=\cos(y+f(x))[/math]

 

here y and f are functions of x .

 

highly non linear. tried maple. didnt give jack

I know it's a long shot, but the first thing that springs to mind is a Taylor expansion of cos? Might be worth a shot, although looking at it, it might not do any good.

I know it's a long shot, but the first thing that springs to mind is a Taylor expansion of cos? Might be worth a shot, although looking at it, it might not do any good.

good idea . will give it a go. then i assume the the solution will be a series solution. it is rigorous to change the order of integration and sum of a series.

 

i.e is

 

[math]\int (\sum a_n)=\sum(\int a_n)[/math]?

good idea . will give it a go. then i assume the the solution will be a series solution. it is rigorous to change the order of integration and sum of a series.

 

i.e is

 

[math]\int (\sum a_n)=\sum(\int a_n)[/math]?

you have two different unknowns: y and f, so you don't appear to have enough information to produce a solution with only one equation.

you have two different unknowns: y and f, so you don't appear to have enough information to produce a solution with only one equation.

f will be given..

 

so just want to find y in terms of that f along with composition of other fucntions

f will be given..

 

so just want to find y in terms of that f along with composition of other fucntions

Another idea that occurred might be to use Fourier transforms, but similarly to the other problem, I don't know whether that would help any (because f is just an arbitrary function).

if you want to have it in terms of y replace f(x) with u

 

then you have dy/dx=cos(y+u)

which is equal to

dy/dx=cos(y)cos(u)-sin(y)sin(u)

 

thats as far as I can go hope it helps

Maybe you can find something that'll differentiate to give that angle addition?